Abstract
We compute the renormalisation factors (Z-matrices) of the ΔF = 2 four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with nf = 2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to overline{mathrm{MS}} , the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper [1]. We argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.
Highlights
We compute the renormalisation factors (Z-matrices) of the ∆F = 2 fourquark operators needed for Beyond the Standard Model (BSM) kaon mixing
We argue in this work that at this point, results obtained using the regularisation independent (RI)-MOM scheme should be approached with skepticism or, if possible even discarded, at least for these quantities
In this work we have defined and investigated new RI-SMOM intermediate schemes for the renormalisation of ∆F = 2 four-quark operators needed for neutral kaon mixing beyond the standard model studies
Summary
We denote ZRI the corresponding renormalisation factor computed on the same lattice (following the Rome-Southampton method) in a regularisation independent (RI) scheme. For example in a typical phenomenological application the hadronic matrix element has to be combined with a Wilson coefficient C(μ) computed in continuum perturbation theory (the hadronic matrix element describes the long-distance effetcts and the Wilson coefficient the short-distance ones). Both of these must be computed in a common scheme, MS, to be matched to a physical quantity. We remind the reader that the renormalisation is performed nonperturbatively, the matching to MS from the RI scheme (RMS←RI(μ)) has to be done using continuum perturbation theory as MS is not possible to implement on the lattice
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